26 citations · 54 across the 15 of their papers we have counts for
4 papers · 1 filter
Nakayama functors for coalgebras and their applications to Frobenius tensor categories
Taiki Shibata, Kenichi Shimizu
We introduce Nakayama functors for coalgebras and investigate their basic properties. These functors are expressed by certain (co)ends as in the finite case discussed by Fuchs, Sch…
Affine Kac-Moody groups and Lie algebras in the language of SGA3
Jun Morita, Arturo Pianzola, Taiki Shibata
In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groups play a distinguished role due to their many applications to various areas of mathematics and physic…
Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations
Jun Morita, Arturo Pianzola, Taiki Shibata
We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations.
Modified traces and the Nakayama functor
Taiki Shibata, Kenichi Shimizu
We organize the modified trace theory with the use of the Nakayama functor of finite abelian categories. For a linear right exact functor on a finite abelian category $\mathcal…